Generally, sigma-delta modulation (SDM) refers to a process of encoding high resolution signals, such as analog signals, into lower resolution signals, such as digital signals, using pulse-density modulation (PDM). PDM refers to a form of modulation where analog signals are represented with digital data such that the signal resulting from pulse-density modulation expresses the analog signal's amplitude through its relative bit density. Sigma-delta demodulation refers to the inverse process of reconstructing the analog signal from the lower resolution digital signal. Commonly, sigma-delta modulation and demodulation is employed by analog-to-digital converters (ADC's), digital-to-analog converters (DAC's), frequency synthesizers, switched-mode power supplies, control circuits for class-D amplifiers and motor controls to name a few examples.
A sigma-delta modulator is constructed as a linear combination of an integrator unit and a quantizer unit where the output of the integrator unit feeds into the input of the quantizer unit. The output of the quantizer unit is the output signal of the sigma-delta modulator. This output also is part of a feedback loop that feeds the output signal back to a summation unit whose output is fed to the input of the integrator unit. This summation unit, integrator unit and quantizer unit forms what is commonly referred to as a first order sigma-delta modulator. Adding additional integrator units in-line before the summation unit increases the order by one for each additional integrator added in-line before the summation unit.
To achieve a desired signal-to-noise ratio (SNR), such as a 90 to 100 dB SNR, for the output signal of a sigma delta modulator, the sigma-delta modulator may be modified in two ways. In a first way, the order of the sigma-delta modulator may be increased, although increasing the order above a fourth or fifth order generally results in an unstable sigma-delta modulator. In the second way, the oversampling rate (OSR) of the sigma-delta modulator may be increased. However, increasing the OSR of the sigma-delta modulator increases the number of bits required to accurately represent the input signal. Increasing the number of bits may be a significant consideration in sigma-delta modulator applications that communicate the output signal over a limited bandwidth channel, such as a wireless channel in which sigma-delta modulators may be employed in analog-to-digital (A/D) converters or digital-to-analog (D/A) converters in mobile phones. The increase of bits may consume more wireless channel bandwidth.